fuzzylogic #1

[Logical Language Group <lojbab@ACCESS.DIGEX.NET>]

>From:         "Steven M. Belknap" <sbelknap@UIC.EDU>
>Subject:      fuzzy truth
>
>I would still like to be able to say something like:
>
>The food at Le Francais in Wheeling Illinois is 8ish on a 0 to 9 scale.
>It is possible that there is some easy way to do this already in lojban,
>although I haven't seen any posts that quite get at what I want to do.
>As I've written before, I believe this issue of fuzziness is important
>because it is closer to how most people actually think about the world.
>Often people are forced into an Aristotlean straitjacket which does not
>correspond to what they mean.

Well, Cowan wanted some good examples of "ni".  I think we have them
here.

li ji'ibi li nobi'oga'oso cu ni le cidja pe vi la'o fy Le Francais fy pe
vi la .uilin. ilyNOIS. cu xamgu kei

Approximately 8 on a scale from 0..9 inclusive is the amount that the
food at ... is good.

which could probably be shortened to

li ji'ibi li so cu ni...

Approximately 8 on a scale of 9 is the amount that the food at ... is
good.

All this assuming that the scale is of goodness, and not of foodishness
which would change the inside of the "ni"

>For example, using the legal setting:
>
>"Did you or did you not see the defendant defenestrate the errant
>politician?"
>
>Now, perhaps I saw some shadows which on a 0 to 7 scale I am 4ish
>certain corresponded to the defendant and the errant politician, and
>suppose I saw these shadows perform the alledged defenestration to
>certainty 3ish on a 0 to 4 scale.  If I attempt to answer this question
>yes/no, I will be dissatisfied with my answer.  If I equivocate, I will
>be accused by the obnoxious lawyer that I am equivocating, and he will
>attempt to force me into a falsely dichotomous Aristotlean universe of
>reply.

li vo li ze ni le se viska be mi ctino (pe vi le zekri) cu ctino le se
xusra zungi (vi le zekri)
.i li ci li vo cu ni le se ctino cu cankypagryzukte le naldrani
turnyzukte

4 on a scale of 7 is the amount that the seen by me shadow (at the
crime) were shadows of the assertedly guilty. and 3 on a scale of 4 is
the amount that the beshadowed one window-pass_through_agented the
incorrect governing_agent.

>It would be nice if fuzzy replies would elegantly, compactly allow for
>this sort of thing.  There have been several objections:

Not sure what is elegant and compact, but the verbosity in the above was
in expressing the claim and not in expressing the fuzziness.

Maybe we could conventionally shorten such a claim by doing

mi pu viska sela'u li ci tela'u li vo lenu le ctino be le se xusra zungi
be'o pe sela'u li vo zi'e tela'u li ze cu cankypagryzukte le naldrani
turnyzukte

I saw (3 on a scale of 4) the event of (the shadow of the assertedly
guilty) (4 on a scale of 7) window-pass_through_agent the incorrect
governing_agent.

or even

mi pu cifi'uvocu'o viska lenu le vofi'uzecu'o ctino be le se xusra zungi
cu cankypagryzukte le naldrani turnyzukte

I 3/4-chance saw the event of the 4/7=chance shadow of the assertedly
guilty window-pass_through_agent the incorrect governing_agent.

>1. People don't think this way.  This is the way computers handle
>fuzziness.

I'll agree - you broke the fuzziness down one step finer than I would
expect.  But I coped.

>The use of numbers in my examples is not meant to imply exactness-these
>numbers are fuzzy.  One example I see in my medical practice is when I
>ask a patient to describe the severity of pain.
>
>"How bad does it hurt?"  "Well, doc, its about a 3 on a 1 to 10 scale."

You can put ji'i before any of those numbers to express inexactness.

>2. We can handle this with a sequence of je' things, as suggested by xorxes:
>je'ucai
>je'u(sai)
>je'uru'e
>je'ucu'i
>je'unairu'e
>je'unai(sai)
>je'unaicai
>
>There are two problems with these types of schemes:
>
>First, the granularity is fixed.  If I want to use a 3 point fuzzy scale
>(yes, maybe, no) for reasons of being purposely less precise than a 5
>point fuzzy scale, (yes, probably, maybe, possibly, no) then I can't get
>across the intentional choice of greater granularity of my reply with
>the je' schemes.
>
>Second, there is no specification of ordinality.  I think ordinality is
>quite useful, as it seems important in expressing fuzziness.  Je'uru'e
>and the other je' things are not obviously distributed in an even way
>along the truth scale.

You obviously wouldn't use this scale for expressing that kind of
fuzziness.  The values, BTW ARE fuzzy, and I think fuzziness equates to
not being necessarily evenly distributed along the truth scale.  For
example, if you rate movies on a 1-10 scale, I'll bet that there will be
clumps in a statistical sample clustering around certain points.
Indeed, we have the magic number 7 embedded in our scales representing
the purported number of distinct "objects" (in this case places on the
scale) that can be kept in mind at one time.

>3. You can actually say what you mean in lojban quite exactly by stating
>the whole thing in mathematical terms.
>
>I want to include ordinality, fuzziness, and granularity in my fuzzy
>statements.  Expressing all three concepts with the lojban constructs I
>know is longwinded, unwieldy, and probably incomprehensible.

I think my most abbreviated form should be comprehensible, and the
others probably are as well.

>I doubt that such constructions would be used very often.  Because
>lojban is based on the predicate calculus, logic, and careful attention
>to semantics, I think lojban is potentially vulnerable to this problem
>of one speaker forcing false dichotomies on other speakers, and that a
>rich fuzzy logic mechanism is required.  I remember discussing this with
>lojbab when I visited him several months ago, and I came away from our
>discussion convinced that this would not require any sort of major or
>even minor change in the language.  Maybe using inexact numbers would be
>a start:
>
>li piso'u to li piro

That one would work, but has only a granularity of 6 evenly spaced, with
"da'a" thrown in there as a wild point just short of "ro".

>The closest gismu for fuzzy would seem to be <kerfa>
>
>x1 is a/the hair/| [body-part] of x2 at body location x3

Only for the most malglico minded!  I hope you are trying to make a pun,
since this is most unseemly a metaphor for a logical language, and you
otherwise seem to have Lojbanic concetps down quite fine.

You used the right metaphor above in explaining things:  nalsatci (=
inexact), which can apply to any of the approaches, or ckilyninjetnu (=
scalar amount-of-truth) if you don't want to insist on approximate
numbers.

>Although <kerfa> seems to be referring to animals (or perhaps the
>leftover pizza in the back of my refrigerator), couldn't it also be used
>for the idea of fuzzy sets or fuzzy logic?
>
><X1> <kerfa> <fuzzy numerator> <fuzzy denominator>

I hope not, unless the numbers start growing fur %^)

>If this is unsatisfactory, how about a lujvo or le'avla for fuzzy?

tu'a le nu zukte cu za'o se cpedu

The act is too-long-beyond-completion being requested.

lojbab